Mathematical induction: principles of mathematical induction and theorems and its applications, problems on divisibility.

3. LINEAR EQUATIONS:

Linear equations in two variables: System of linear equations ,Simultaneous equation in two variables, Dependant equations, Linear equations and their graphs, Linear functions , System of equations, linear programming-problems (LPP). The fundamental theorem, graphical method of solving an LPP, a closed converse polygon, general graphical methods – application of LPP.

In-equations: Linear in-equations and their graphs, System of in-equations. Linear equations in two variables, System of linear equations, simultaneous equation in two variables Dependant equations, linear equations and their graphs, linear functions, system of equations, System of two points, which is not parallel to X-axis, Midpoint of the segment following A(x1,y1), B(x2,y2) equation of a line passing through the origin having slope m, The slope intercept form of a line, the point slope form of a line, the intercept form of a line, the two point form of a line, linear in-equations, their graphs, system of linear in-equations.

Quadratic expressions, equations in one variable, sign of quadratic expressions, changes in signs and maximum and minimum values, quadratic in-equations, relation between the roots and the coefficient in an equation, remainder theorem, connecting problems, solving an equation when two or more of its roots are connected by Cartesian relations, Horner’s method of synthetic division, trial and error method, Procedure to find multiple roots.

4. GEOMETRY

Structure of geometry, axioms, Historical background, Basic axioms, Parallel line, theorems, triangles and polygons, angles of a polygons, theorems based on, Polygon congruence of triangle SAS, ASA, SSA, axioms, Parallelogram and its properties, Triangles, Particular types, geometric inequalities in a triangles some theorem, circles and concurrent lines in triangles, Theorems based on circles, Concurrent lines in a triangle, Median, Altitudes of a triangle, line of symmetry, axis of symmetry, point symmetry, image of an angle.

Quadrilaterals, example of different Quadrilaterals, Parallel lines and triangles, theorems, intercept, Theorems, locus, points equidistant from two given points. Theorems, an concurrency, attitude, circum centre, ortho centre, centroid, Areas, polygonal region, Area axiom, congruent axiom, area monotonic axiom, area of parallelogram theorem, Area of Triangle, Theorem based quit, circles are of a circle, semi circle, segment of a circle, Congruence of a circle, Theorems based on circle.

Similar polygons, similar triangle and their properties, Basic proportionality theorem, vertical angle bisection theorem, Similar Triangle, AAA similarity, SSA, SAS similarities Pythagoras theorem, Tangents to a circle, different properties of a tangent to a circle, segments of a chord, Common tangents to two circles.

Square, rectangle, triangle, Quadrilateral, Circle, Ring (Annulus), Sector. Prism, total surface area of right prism, volume of a prism, Volume of a cube, Cuboids, The right pyramid, Cylinder, Hollow cylinder, Cylindrical shell, ratio’s of cylinders, cone, Hollow cone, solid cone, Curved surface area, total surface area, volume of a right circular cone, Sphere: Surface area of a sphere, total surface area of a hemisphere, Volume of a sphere, Hollow hemisphere.

6. MATRICES

Matrix Definition, Order of a matrix, Types of matrices, Equality of two matrices, Addition, Subtraction, multiplication of matrix, Product of two matrices, properties of products of matrices, transpose of matrix, properties, skew symmetric matrix, Adjoint and inverse of a matrix, simultaneous linear equations, types of system of simultaneous linear equations, consistency and inconsistency of Simultaneous equation. .

Multiplicative inverse of a square matrix, singular and non singular matrix, solution of a system of linear equations in two variable using matrices determinants, properties of determinants, Matrix inverse method and Cramer’s , Inversion and Gauss Jordan method and Solving Equations Triangle matrices, properties of addition of matrices, sector multiple of a matrix

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